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WITH a dream of competing at the Olympics, Hamilton's Amy Williams is one step closer after being selected to represent Victoria at the National Equestrian Interschool Championships.
After attending the Victorian State Equestrian Interschool Championships last week in Werribee and taking out the primary school 90 centimetre show jumping championships, Amy is one of two selected to represent Victoria.
Only 11-years-old, the St Mary's Primary School student said she had been riding since she was five and did so because it was fun.
Full story in The Spectator on Saturday, July 12, 2014, or subscribe to our epaper at top of page. Only $2 per week.


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The Old Testament. Biblical philosophy is not an abstract monologue but a dialogue with God. The Bible never attempts to prove the existence of God, bur starts from the premise that God exists (i.e., Gen 1:1 ); philosophy, in contrast, takes up questions concerning the nature of the universe and existence that do not necessarily presume the verity of God. Therefore, philosophy can be an effective tool if properly used as a means of understanding pretheological questions, but not as a method of supplanting the revelation already made available by faith through God's Scriptures. The limitations of human reason, especially in light of the moral degeneracy in humans, requires God's help in resolving philosophical questions.
The sacrificial structure of the Hebrew Scriptures reveals a simple, nonesoteric approach to the questions concerning solidarity with God and oneself. Faith was a prerequisite for abiding in the covenant. There is rarely a philosophical concern, although in the psalms occasionally deeper questions concerning the afterlife are considered in the light of theodicy.
The New Testament. It is not surprising that Paul, "the apostle to the Gentiles, " is more philosophical and deals with the problem of onerous philosophy more than any other writer in the New Testament because of the pragmatic issues of polytheism and atheism he confronted. The only time the world "philosophy" is used in the Bible is in Colossians 2:8. The problem addressed by Paul is probably an incipient form of gnosticism. One fascinating aspect of this passage is the idea that one can be taken "captive" through philosophy. Paul is not anti-intellectual, as is evidenced by the fact that he quotes Greek poets in Acts 17:28; also, in Acts 17 he directs his teachings toward Epicurean and Stoic philosophers, which shows that he was knowledgeable of their philosophy. He even agreed with it where he could. But, when the apocalyptic element is understood, it becomes clearer the philosophical deficiency that Paul was pointing out. The recipients of the second-person plural pronoun in Colossians 2:8 are Gentiles (e.f., 1:27 ). The philosophy is more clearly spelled out in 2:16: "Therefore do not let anyone condemn you in matters of food and drink or of observing festivals, new moons, or sabbaths" (NRSV). Food laws and calendar observance were not required for the Gentiles' newfound faith. The observance of these nationalistic requirements was synonymous with being under the influence of "elemental spirits of the universe, " that is, the evil spirits that swarmed the cosmos. To be under this demonic influence was not necessary because Christ "disarmed the rulers and authorities and made a public example of them, triumphing over them in it" ( Col 2:15 ).
Another aspect of the philosophy was esoteric speculation. Two examples are given: "worship of angels" and "dwelling on visions." Hebrews 1 also addresses the problem of the worship of angels (Christ was erroneously thought to be an angel). In Colossians, Paul contrasts arrogant, earthly, speculative philosophy with humble, transcendental, and righteous philosophy derived from God.
The problem of exploitative philosophy in Colossians 2:8 is not simply an aversion toward a theory of analysis underlying deportment, thought, knowledge, and the constitution of the universe. Rather, it is unwarranted speculation that encroaches on the freedom of another. The regulations "do not handle, do not taste, do not touch" (v. 21) reveal that a personal, introspective analysis concerning one's desire for meaning is not in view, but a philosophy that requires a change in behavior in another. It is the type of conjecture that places cultural, not moral demands on one and begins with the supposition of ethnic and religious superiority. This predicament was precisely the quandary of gnosticism. The elitism that proliferated gnosticism was largely based on the philosophical premise that gnostics were superior and held a secret knowledge.
The term "philosopher" (literally "lover of wisdom") appears in Acts 17:18. It is clear that the first time Christianity was taught in Athens, an intellectual hub of the ancient world, the message of monotheism was equated with obtuseness. Ironically, much of their philosophy was derived from superstition.
Epicurean philosophy originated from its founder Epicurus, who died in 270 b.c. Epicureans did not believe in an afterlife; therefore, one should neither fear death nor believe in supernatural beings. There was no jurisdiction over the state of affairs of humans. That which brought the most felicity now was the highest aim in life. Unlike the Stoics, the Epicureans rejected fate because there were no governing principles or beings that controlled one's destiny. The body was an indispensable part of human nature. Eventually, against the concept envisaged by Epicurus, this philosophy became associated with hedonistic practices because there was no infinite reference point to dictate morality.
Stoic philosophy was founded by Zeno around 300 b.c. In contrast to Epicurean philosophy, individuals achieve well-being and peace through their consonance with nature (which was in a constant state of change) by having the qualities of bravery, justice, self-control, and a competent intellect. All people have the divine spark of godhood (i.e., the logos) within them. Stoicism was monistic or even pantheistic because of the belief that divinity was so immanent that nature itself was part of the divine spark.
Therefore, providence governed the affairs of humans. The form of Stoic philosophy found in the New Testament was amalgamated with Roman polytheism. Paul was "deeply distressed" because the city was "full of idols." Undoubtedly, some of these idols were worshiped by the Stoics (not the Epicurean atheists).
Paul's sermon is directed toward Stoic and Epicurean philosophy. Addressing Stoic fatalism, he points out that God created the world and does not dwell in idols ( 17:24 ). Unlike Stoic pantheism, God "gives to all mortals life and breath and all things" (v. 25). God is not so immanent that he is the creation itself.
Unlike the Epicureans, Paul announces that God requires repentance by all (v. 30) "because he has fixed a day on which he will have the world judged in righteousness" (v. 31). The resurrection of Christ is the "assurance" that all will raise from the dead and stand before God (v. 31). The resurrection of Christ, with the subsequent philosophical and logical argument that Paul makes in 1 Corinthians 15, stands in sharp contrast to hedonistic Epicureanism. Like Colossians 2, Acts 17 demonstrates how philosophy, erroneously applied, can lead to "captivity" (e.g., Epicurean hedonism) and the control of "elemental spirits of the universe" (e.g., Stoic idolatry).
Even though Paul's philosophy in Acts 17 is logical, it is not acrimonious. Paul practices the principle he sets forth in 1 Corinthians 9:22: "I have become all things to all people, that I might by all means save some." The fact that Paul quotes some of their poets (17:28) corroborates the notion that he was not anti-intellectual; instead, he gives a reasonable, philosophical deposition when challenging the intellectuals of Athens.
Another example of Paul's cultural sensitivity can be found in Acts 19:9. Paul argued in the Hall of Tyrannus in Ephesus for two years. Tyrannus was probably a school named after a Greek philosopher. The Jewish apostle to the Gentiles was undoubtedly skilled in Greek rhetoric and philosophy.
In Romans 1:18-23 Paul's philosophical logic is essential a "teleological" argument, that is, a testimony of the existence of God based on the order and purpose of the universe. Paul uses philosophical reasoning to discredit pagan superstition.
Eric W. Adams
Bibliography. J. Guttmann, Philosophies of Judaism: The History of Jewish Philosophy from Biblical Times to Franz Rosenzweig; J. Hick, ed., Classical and Contemporary Readings in the Philosophy of Religion; C. S. Lewis, The Problem of Pain; G. Vesey, ed., The Philosophy in Christianity; H. A. Wolfson, The Philosophy of the Church Fathers.
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It is the object of the following article to give some account (I.) of that development of thought among the Jews which answered to the philosophy of the West; (II.) of the systematic progress of Greek philosophy as forming a complete whole; and (III.) of the contact of Christianity with philosophy. I. THE PHILOSOPHIC DISCIPLINE OF THE JEWS. --Philosophy, if we limit the word strictly to describe the free pursuit of knowledge of which truth is the one complete end is essentially of western growth. In the East the search after wisdom has always been connected with practice. The history of the Jews offers no exception to this remark: there is no Jewish philosophy, properly so called. The method of Greece was to proceed from life to God; the method of Israel (so to speak) was to proceed from God to life. The axioms of one system are the conclusions of the other. The one led to the successive abandonment of the noblest domains of science which man had claimed originally as his own, till it left bare systems of morality; the other, in the fullness of time, prepared many to welcome the Christ --the Truth. The philosophy of the Jews, using the word in a large sense, is to be sought for rather in the progress of the national life than in special books. Step by step the idea of the family was raised into that of the people; and the kingdom furnished the basis of those wider promises which included all nations in one kingdom of heaven. The social, the political, the cosmical relations of man were traced out gradually in relation to God. The philosophy of the Jews is thus essentially a moral philosophy, resting on a definite connection with God. The doctrines of Creation and Providence, of an infinite divine person and of a responsible human will, which elsewhere form the ultimate limits of speculation, are here assumed at the outset. The Psalms, which, among the other infinite lessons which they convey, give a deep insight into the need of a personal apprehension of truth, everywhere declare the absolute sovereignty of God over the material and the moral world. One man among all is distinguished among the Jews as "the wise man". The description which is given of his writings serves as a commentary on the national view of philosophy ( 1 Kings 4:30-33 ) The lesson of practical duty, the full utterance of "a large heart," ibid. 29, the careful study of Gods creatures, --this is the sum of wisdom. Yet in fact the very practical aim of this philosophy leads to the revelation of the most sublime truth. Wisdom was gradually felt to be a person, throned by God and holding converse with men. ( Proverbs 8:1 ) ... She was seen to stand in open enmity with "the strange woman"), who sought to draw them aside by sensuous attractions; and thus a new step was made toward the central doctrine of Christianity: --the incarnation of the Word. Two books of the Bible, Job and Ecclesiastes, of which the latter at any rate belongs to the period of the close of the kingdom, approach more nearly than any others to the type of philosophical discussions. But in both the problem is moral and not metaphysical. The one deals with the evils which afflict "the perfect and upright;" the other with the vanity of all the pursuits and pleasures of earth. The captivity necessarily exercised a profound influence. The teaching of Persia Jewish thought. The teaching of Persia seems to have been designed to supply important elements in the education of the chosen people. But it did yet more than this. The contact of the Jews with Persia thus gave rise to a traditional mysticism. Their contact with Greece was marked by the rise of distinct sects. In the third century B.C. the great Doctor Antigonus of Socho bears a Greek name, and popular belief pointed to him as the teacher of Sadoc and Boethus the supposed founders of Jewish rationalism. At any rate we may date from this time the twofold division of Jewish speculation, The Sadducees appear as the supporters of human freedom in its widest scope; the Pharisees of a religious Stoicism. At a later time the cycle of doctrine was completed, when by a natural reaction the Essenes established as mystic Asceticism. II. THE DEVELOPMENT OF GREEK PHILOSOPHY. --The various attempts which have been made to derive western philosophy from eastern sources have signally failed. It is true that in some degree the character of Greek speculation may have been influenced, at least in its earliest-stages, by religious ideas which were originally introduced from the East; but this indirect influence does hot affect the real originality of the Greek teachers. The very value of Greek teaching lies in the fact that it was, as far as is possible, a result of simple reason, or, if faith asserts ifs prerogative, the distinction is sharply marked. Of the various classifications of the Greek schools which have been proposed, the simplest and truest seems to be that which divides the history of philosophy into three great periods, the first reaching to the era of the Sophists, the next to the death of Aristotle, the third to the Christian era. In the first period the world objectively is the great centre of inquiry; in the second, the "ideas" of things, truth, and being; in the third, the chief interest of philosophy falls back upon the practical conduct of life. After the Christian era philosophy ceased to have any true vitality in Greece, but it made fresh efforts to meet the conditions of life at Alexandria and Rome.
fi-los'-o-fi (philosophia):
1. Definition and Scope
(1) Intuitive Philosophy Is Universal
(2) Speculative Philosophy Belongs Mainly to Western Thought
2. Greek Philosophy
3. Philosophy in Old Testament and Judaism
(1) Of Nature
(2) Of History
(3) Post-exilic
(4) Alexandrian
4. Philosophy in the New Testament
(1) The Teaching of Jesus Christ
(2) Apostolic Teaching
(3) Attitude of New Testament Writers toward Philosophy
1. Definition and Scope:
Only found in Colossians 2:8; literally, the love and pursuit of wisdom and knowledge. In its technical sense, the term is now used for the conscious endeavor of thought, by speculative process, to interpret the whole of human experience, as a consistent and systematic unity, which would be the ultimate truth of all that may be known. The term is also used, in a wider sense, of all interpretations of experience, or parts of experience, however obtained, whether by revelation, intuition or unconscious speculation. No hard-and-fast line can be drawn between the two kinds of philosophy. Some of the ruling conceptions of speculation, such as God, spirit, order, causation, true and false, good and evil, were not discovered by reason, but given in experience.
(1) Intuitive Philosophy Is Universal.
The human mind has always and everywhere furnished itself with some kind of explanation of the universe. From the lowest animism and fetishism up to the higher religions, ideas are found which served men as explanations of those features of experience which attracted their attention. They were often regarded as given by vision, intuition or some other method of revelation. In the higher religions, the mind reflected upon these ideas, and elaborated them into systems of thought that bear some resemblance to the speculative theories of western thought. In China, both Confucianism and Taoism developed theories of human life and destiny that bear some resemblance to Stoicism. The religions of Assyria and Babylonia enshrined in their legends theories of the world and of man and his institutions. In India, men's belief in the Nature-gods gradually developed into pantheistic Brahmanism, which reduced the multiplicity of experience into one ultimate being, Brahma. But the desire for moral salvation and the sense of pain and evil produced a reaction, and led to the pessimistic and nihilistic philosophy of Buddhism. In Persia, the moral consciousness awoke earlier, and the attempt to systematize the multiplicity of polytheism issued in the dualistic philosophy of later Zoroastrianism. The whole realm of being was divided into two kingdoms, created and ruled by two lords:
Ahura Mazda, the creator of light and life, law, order and goodness, and Anro Mainyus, the author of darkness, evil and death. Each was surrounded by a court of spiritual beings kindred to himself, his messengers and agents in the world (see PERSIAN RELIGION (ANCIENT)). Of all these religious philosophies, only those of Assyria and Babylonia, and of Persia, are likely to have come into any contact with Biblical thought. The former have some affinity with the accounts of creation and the flood in Genesis; and the influence of the latter may be traced in the dualism and angelology and demonology of later Judaism, and again in the Gnostic systems that grew up in the Christian church, and through both channels it was perpetuated, as a dualistic influence, in the lower strata of Christian thought down through the Middle Ages.
(2) Speculative Philosophy Belongs Mainly to Western Thought.
It arose in Greece about the beginning of the 6th century BC. It began with the problem of the general nature of being, or ontology. But it was soon forced to consider the conditions of knowing anything at all, or to epistemology. These two studies constitute metaphysics, a term often used as synonymous with philosophy in the stricter sense. Speculation about ideal truth again led to inquiries as to the ultimate nature of the kindred ideas of the good (ethics) and the beautiful (aesthetics). And as these ideas were related to society as well as to the individual, the Greeks developed theories of the ideal organization of society on the basis of the true, the good and the beautiful, or politics and pedagogics. The only branch of speculation to which the Greeks made no appreciable contribution was the philosophy of religion, which is a modern development.
The progress of philosophy in history divides itself naturally into three main periods:
(a) ancient, from the 6th century BC to the 3rd century AD, when it is almost exclusively Greek, with some practical adaptations of Greek thought by Roman writers; (b) medieval, from the 3rd to the 16th century, where some of the ruling conceptions of Greek thought were utilized for the systematization of Christian dogma, but speculation was mainly confined within the limits of ecclesiastical orthodoxy; there were, however, some independent Arabian and Jewish speculations; (c) modern, from the 16th century to the present time, in which thought becomes free again to speculate upon all the problems presented by experience, though it only realized its liberty fully in the hands of Locke, Hume and Kant.
2. Greek Philosophy:
Greek philosophy was the only speculative system that could have had any influence upon Biblical thought. Its main development was contemporaneous with the later Old Testament writers, but the two peoples were in every way so remote one another that no interchange of ideas was probable.
During the last two centuries BC, Greek thought spread so widely that it came to dominate the cultured thought of the world into which Christianity entered, and it would have been strange if no trace of its influence were found in the New Testament. In the first stage of its development, from Thales to Socrates, it was concerned almost entirely with attempts to explain the nature of reality by reducing the phenomenal world into some one of its elements. Socrates changed its center of gravity, and definitely raised the problems of morality and knowledge to the position of first importance. His principles were developed by Plato into a complex and many-sided system which, more than any other, has influenced all subsequent thought. He united ultimate reality and the highest good into one supreme principle or idea which he called the Good, and also God. It was the essence, archetype and origin of all wisdom, goodness and beauty. It communicated itself as intermediary archerypal ideas to produce all individual things. So that the formative principles of all existence were moral and spiritual. But it had to make all things out of preexisting matter, which is essentially evil, and which therefore was refractory and hostile to the Good. That is why it did not make a perfect world. Plato's system was therefore rent by an irreconcilable dualism of mind and body, spirit and matter, good and evil. And his mediating ideas could not bridge the gulf, because they belonged only to the side of the ideal. Aristotle was Plato's disciple, and he started from Plato's idealistic presuppositions, but endeavored to transcend his dualism. He thus applied himself to a closer and more accurate study of actual experience, and added much to the knowledge of the physical world. He organized and classified the methods and contents of knowledge and created the science of logic, which in the Christian Middle Ages became the chief instrument of the great systematic theologians of the church. He tried to bring Plato's ideas "down from heaven," and to represent them as the creative and formative principles within the world, which he conceived as a system of development, rising by spiritual gradations from the lower to the higher forms, and culminating in God, who is the uncaused cause of all things. But underneath all the forms still remained matter as an antithetical element, and Aristotle rather concealed than solved the dualism of Plato.
Meanwhile, the moral principles of Socrates were being developed with a more directly ethical interest, by the Cyrenaics and Epicureans, into a system of Hedonism, and, by the Cynics and Stoics, into a doctrine of intuitive right and duty, resting inconsistently upon a pantheistic and materialistic view of the universe. But the spiritual and ethical elements in Stoicism became only second to Platonism in the preparation of the Greek world for Christianity. During the last two and a half centuries BC, Greek philosophy showed signs of rapid decline. On the one hand, Pyrrho and his school propounded a thoroughgoing skepticism which denied the possibility of all knowledge whatsoever. On the other hand, the older schools, no longer served by creative minds, tended to merge their ideas into a common eclecticism which its teachers reduced into an empty and formal dogmatism. The most fruitful and fateful product of Greek thought in this period was its amalgamation with Jewish and oriental ideas in the great cosmopolitan centers of the Greek world. There are evidences that this process was going on in the cities of Asia, Syria and Egypt, but the only extensive account of it remaining is found in the works of Philo, the Jewish philosopher of Alexandria (see PHILO, JUDAEUS). He tried to graft Plato's idealism upon Hebrew monotheism.
He starts with Plato's two principles, pure being or God, and preexisting matter. In his endeavor to bridge the gulf between them, he interposed between God and the world the powers of God, goodness and justice; and to gather these into a final unity, he created his conception of the Loges of God. In the formation of this conception, he merged together the Platonic idea of the good, the Stoic world-reason, and a number of Jewish ideas, the glory, the word, the name, of God, the heavenly man and the great high priest, and personified the whole as the one mediator between God and the world. Christian thought laid hold of this idea, and employed it as its master-category for the interpretation of the person of Christ.
See LOGOS.
3. Philosophy in Old Testament and Judaism:
There is no speculative philosophy in the Old Testament nor any certain trace of its influence. Its writers and actors never set themselves to pursue knowledge in the abstract and for its own sake. They always wrought for moral purposes. But moral activity proceeds on the intellectual presuppositions and interpretations of the experiences within which it acts. Hence, we find in the Old Testament accounts of the origin and course of nature, a philosophy of history and its institutions, and interpretations of men's moral and religious experiences. They all center in God, issue from His sovereign will, and express the realization of His purpose of righteousness in the world.
See GOD.
(1) Of Nature:
All nature originated in God's creative act (Genesis 2) or word (Genesis 1). In later literature the whole course and order of Nature, its beauty and bounty, as well as its wonders and terrors, are represented as the acts of God's will (Isa 40; 41; 42; 43; 44; 45; Ps 8:19; 29; 50; 65; 68; 104, etc.). But His action in Nature is always subordinated to His moral ends.
(2) Of History:
Similarly, the course and events of the history of Israel and her neighbors are the acts of Yahweh's will (Amos 1; 2; Isaiah 41:2; 43:3; 45:9,10,14) In the historical books of Samuel and Kings, and still more of Chronicles, all the events of history are represented as the acts of God's moral government. In a more general way, the whole of history is set forth as a series of covenants that God, of His free grace, made with man (see COVENANT). The Noachic covenant fixed the order of Nature. The covenant with Abraham, Isaac and Jacob accounted for the origin and choice of Israel. The covenants with Moses and Aaron established the Law and the priesthood, and that with David, the kingship. And the hope of the future lies in the new covenant (Jeremiah 31:31-35). God's covenants were all acts of His sovereign and gracious will.
(3) Post-exilic:
In post-exilic times, new experiences, and perhaps new intellectual influences, drove the Jews to probe deeper into the problem of existence. They adhered to the cardinal principle of He thought, that God's sovereign will, working out His purpose of righteousness, was the first cause of all things (see RIGHTEOUSNESS). But they found it difficult to coordinate this belief with their other ideas, in two ways. Ethical monotheism tended to become an abstract deism which removed God altogether out of the world. And the catastrophes that befell the nation, in the exile and after, raised the problem of suffering and evil over against God's goodness and righteousness. Therefore in the Wisdom literature we find some conscious speculation on these subjects.
See WISDOM.
(a) The Book of Job discusses the problem of evil, and repudiates the idea that life and history are the process of God's rewards and punishments.
(b) Ecclesiastes comes to the conclusion that all phenomenal experience is vanity. Yet its ultimate philosophy is not pessimistic, for it finds an abiding reality and hope in the fear of God and in the moral life (12:13,14). The same type of thought appears in Ecclesiasticus. Both books have been attributed to the circle of the Sadducees. Some would find in them traces of the influence of Epicureanism.
(c) In Proverbs a more optimistic side prevails. Wisdom is gathered up into a conception or personification which is at once God's friend, His agent in creation, His vicegerent in the world, and man's instructress and guide (chapter 8).
(d) The teaching of the Pharisees especially reveals the tendency to dualism or deism in later Judaism; they interposed between God and the world various agents of mediation, the law, the word, the name, the glory of God and a host of angels, good and bad. They also fostered a new hope of the future, under the double form of the Messianic kingdom, and of resurrection and immortality. How far these tendencies were due to the influence of Persian dualism cannot here be considered.
(e) Essenism represents another effort to get from the world to God by a crude kind of mysticism and asceticism, combined with an extensive angelology.
(4) Alexandrian:
Among the Hellenistic Jews in Alexandria, Aristobulus, the authors of The Wisdom of Solomon and 4 Maccabees, and preeminently Philo, all deal with the two chief problems of Judaism, dualism and evil. But they approach them under the direct influence of Greek thought. The Hebrew idea of wisdom was merged into the Greek conception of the Logos, and so it becomes the mediator of God's thought and activity in the world.
4. Philosophy in the New Testament:
Philosophy appears in the New Testament as intuitive, speculative and eclectic.
(1) The Teaching of Jesus Christ:
Jesus Christ came to fulfill the law and the prophets, and, out of His filial consciousness of God, He propounded answers to the practical demands of His time. His doctrine of God the Father was a philosophy of Nature and life which transcended all dualism. In the kingdom of heaven, the good would ultimately prevail over the evil. The law of love expressed the ideal of conduct for man as individual, and in his relation to society and to God, the supreme and ultimate reality. This teaching was given in the form of revelation, without any trace of speculation.
(2) Apostolic Teaching:
The apostolic writings built upon the teaching and person of Jesus Christ. Their ruling ideas are the doctrines which He taught and embodied. In Paul and John, they are realized as mystical experiences which are expressed in doctrines of universal love. But we may also discover in the apostolic writings at least three strands of speculative philosophy.
(a) Paul employed arguments from natural theology, similar to those of the Stoics (Acts 14:15-17; 17:22-31; Romans 1:19), which involved the principles of the cosmological and teleological arguments.
(b) John employs the Philonic term "Logos" to interpret the person of Christ in His universal relation to God, man and the world; and the main elements of Philo's scheme are clearly present in his doctrine, though here it is no abstract conception standing between God and man, but a living person uniting both (John 1:1-18). Although the term "Logos" is not mentioned, in this sense, in Paul or Hebrews, the Philonic conception has been employed by both writers (Romans 5:8; 8:29; 1 Corinthians 15:24,25; 2 Corinthians 5:18,19; Philippians 2:6; Colossians 1:15-17; 2:9,10; Hebrews 1:1-3,5,6). Paul also expresses his conception of Christ as the manifestation of God under the category of wisdom (1 Corinthians 1:20; 2:7; Ephesians 1:8; Colossians 2:3).
(c) Both in Paul and He appear original speculations designed to interpret individual experience and human history as they culminate in Christ. Paul's interpretation consists of a series of parallel antitheses, flesh and spirit, sin and righteousness, law and grace, works and faith, Adam and Christ. But the author of He adopts the Platonic view that the world of history and phenomena is but the shadow or suggestion of the spiritual and eternal reality which lies behind it, and which partially expresses itself through it.
(3) Attitude of New Testament Writers toward Philosophy:
In the one place in which the term philosophy appears in the New Testament (Colossians 2:8), it seems to mean "subtle dialectics and profitless speculation .... combined with a mystic cosmogony and angelology" (Lightfoot, at the place), the first beginnings of Gnosticism in the Christian church. Paul warns his readers against it, as he also does the Corinthians against the "wisdom" of the Greeks (1 Corinthians 1:19; 2:5,6). A similar tendency may be in view in the warning to Timothy against false doctrines (1 Timothy 1:4; 4:3; 2 Timothy 1:14,16). But with the true spirit of philosophy, as the pursuit of truth, and the endeavor to express more fully and clearly the nature of reality, the spirit and work of the New Testament writers were in complete accord.
Introductions to philosophy by Kulpe, Paulsen, Hoffding, Watson and Mackenzie. Histories of Greek philosophy by Ritter and Preller, Burnet, and Zeller, and of general philosophy by Erdmann, Ueberweg, Windelband and Rogers; E. Caird, The Evolution of Theology in the Greek Philosophies; Hists of the Jews by Schurer, Graetz and Kent; Old Testament Theologies by Schultz and Davidson; New Testament Theologies by Beyschlag and Weinel; Philo's works and treatises thereon by Dahne, Gfrorer and Drummond; Harnack, What Is Christianity? Bigg, The Christian Platonists of Alexandria; Lightfoot, Colossians.
T. Rees
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EARNEST SEWN'S ART SUPPLIES: A quaint corner of London's East End will find a home in New York come April. Denim label Earnest Sewn has tapped the British artist Rob Ryan, who's known for his paper cutout works that feature delicate, silhouetted figures, to re-create his quirky East London shop, Ryantown, in the company's Washington Street store. The installation, called Ryantown USA, will be open for 45 days beginning April 1, in Earnest Sewn's project space at the store. It will spotlight products including an Earnest Sewn T-shirt with a print by Ryan, teddy bears Ryan has customized with Earnest Sewn denim, glassware, bandanas and cushions. Prices for the products haven't been confirmed yet, a spokeswoman for Earnest Sewn said. The pop-up shop also will carry handmade products by Ryan, such as his paper cutout designs and silk screen prints.
"I'm a huge fan of Rob's," said Scott Morrison, founder and designer of Earnest Sewn. "After we had a chance to spend some time with him at his studio in London, it was nearly impossible to imagine us not doing something with him."
Earnest Sewn will launch the project with an event at the store April 1, and the collaborative products also will be sold at Ryan's London store during the installation's run.


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On Wednesday, July 30, House Speaker John Boehner (R-OH) moved to bring suit against President Barack Obama regarding employer-mandate delays as they pertain to the Affordable Care Act. The House voted along party lines 225-201 to move forward with the lawsuit, which authorizes Speaker Boehner to take legal action against the president.
Under the mandate, businesses employing more than 50 workers must provide health care coverage, or pay fines of $2,000 per employee. This mandate was initially supposed to go into effect early this year, but was delayed until 2015. In February, the administration stated that companies employing between 50 and 100 full-time employees will not need to comply until 2016. However, unlike many other administrative rollouts, the statute explicitly stated that the mandate "shall apply to months beginning after December 31, 2013."
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February 1, 2015
BOWLING GREEN, Ky - District tournaments are underway in high school baseball and softball.
In the 14th District Baseball Tournament, Warren Central defeated Warren East 8-2. The Dragons will meet top-seeded Greenwood Tuesday night at South Warren High School.
In the 14th District Softball Tournament, South Warren defeated Warren Central 11-0 in five innings. The Lady Spartans face No. 1 Greenwood in the district semifinals on Tuesday at the WKU Softball Complex.
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They'll soon go from Mr. and Mrs. Smith to Mr. and Mrs. Pitt -- that's right, celebrity supercouple Brad Pitt and Angelina Jolie are finally making it official. A rep for the pair confirmed their news today to THR, calling it "a promise for the future." Really, isn't the long-awaited Brangelina engagement a promise for [...]
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The long wait is finally over, as Angelina Jolie and Brad Pitt welcomed healthy baby twins into the world on Saturday night (July 12). The "Mr. and Mrs. Smith" co-star supercouple are now proud parents of a son and a daughter, Knox ... Read Post
Finally ready to legally declare their love for one another, Angelina Jolie's and Brad Pitt are officially engaged to be married! Following rumors of a planned walk down the aisle sparked by their jeweler, the "Mr and Mrs Smith" co-... Read Post
Post by Lindsay Mannering After hints from a jeweler and a few rumors here and there, Brad Pitt's rep has confirmed to the Associate Press that he and the mother of his six children, Angelina Jolie, are engaged. Hear that? Brad and ... Read Post


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EOS Bodies - For Stills / Re: Canon prevents me from buying the 7D Mark II
« on: October 17, 2014, 12:36:25 PM »How's Vista garbage? People didn't like it because computers were not powerful enough to run it smoothly. Run it on a new recently released computer and it will fly.1. Slow boot times compared to XP, 7 & 8 on like hardware.
2. Worse security than 7 & 8. I shouldn't even need to mention UAC in Vista, but obviously I will. It should conjure a commercial with Justin Long and John Hodgman in your head (http://www.youtube.com/watch?v=FxOIebkmrqs)
3. Atrocious gaming performance.
4. Similarly criminal battery usage on laptops.
5. The driver landscape is somewhat worse since that was the first OS that Microsoft enforced User Mode and Kernel Mode drivers forcing hardware manufacturers to hastily redo their support. However most devices that have Win 7 or 8 drivers can use those drivers in Vista, so this is more of an older hardware problem.
As to Win 7 vs 8, there are some benefits, especially now that you can boot directly to the desktop and skip the whatever-they're-calling-the-touch-interface-this-week. Notably backups, drive mirroring, and file history (essentially version control) is a snap and works really well.
You'll know when you can't get into BIOS with a USB keyboardThere isn't a single BIOS on a motherboard made in the last 4-5 years that doesn't natively support USB mouse and keyboard natively (i.e. during POST). The only situation where this would not be true is someone having disabled USB in the BIOS or a faulty device -- the latter of which would mean you weren't going to be doing anything anyway. If the former is true, a simple reset will solve the problem.
The PS/2 port really just needs to be thrown on the techno trash heap with PCI, 15-pin VGA, and IDE to keep AGP, ISA, and IEEE 1284 ports company.


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Welcome to askonovd's Member Page
See my Clippings See my Journal See my trade list Send me an email
We are ready to begin building our retirement home & garden. Looking forward to retiring, traveling, & of course, Grandchildren!!
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The American people will never knowingly adopt socialism.But under the name of 'liberalism',they will adopt every fragment of the socialist program,until one day America will be a socialist nation,without knowing how it happened - Norman Thomas,6-time presidential candidate for the Socialist Party of America The federal government has taken too much tax money from the people,too much authority from the States,and too much liberty with the Constitution - R. Reagan |
Federal Law Enforcement Agencies Buy Ammunition [nraila.org]
You may recently have seen some in the Internet rumor mill feverishly repeating the obvious truth above, in an effort to stir up fear about recent acquisitions of ammunition by the Department of Homeland Security and a number of smaller agencies. The mildest writers have questioned why seemingly mundane agencies would need ammunition at all; more incendiary authors suggest that these government agencies are preparing for a war with the American people. Much of the concern stems from a lack of understanding of the law enforcement functions carried about by officers in small federal agencies. These agents have the power to make arrests and execute warrants, just like their better-known counterparts at agencies like the FBI. For instance, the Social Security Administration solicited offers for 174,000 rounds of pistol ammunition. But the agency has 295 special agents who combat Social Security fraud that costs tax payers billions each year, so the order works out to roughly 590 rounds of ammunition per agent for training, mandatory quarterly qualification shooting and duty use. More than a few NRA members would use that much ammunition in a weekend shooting class or plinking session. Another recent rumor questioned a request for 46,000 rounds of.40-caliber ammo by the National Oceanic and Atmospheric Administration. NOAA inadvertently fueled that speculation through a clerical error that suggested the ammunition was destined for the National Weather Service. NOAA later clarified that the ammunition was actually for the little known Fisheries Office of Law Enforcement, which enforces laws against illegal fishing and marine life importation. The ammunition is for 63 personnel, amounting to about 730 rounds per officer. The most widespread of the recent rumors involves a Department of Homeland Security contract for a maximum of 450 million rounds of .40-caliber jacketed hollow-points, to be supplied over the next five years. After receiving numerous questions from his constituents regarding the contract, pro-Second Amendment U.S. Rep. Lynn Westmoreland (R-Ga.) and his staff set out in search of the truth. In a press release, Rep. Westmoreland's office explains: If you take the number of agencies that will be using this ammunition – CBP, Citizenship and Immigration Services, the Federal Emergency Management Agency (FEMA), ICE, the U.S. Secret Service, Transportation Security Administration, the DHS police force, and all the guards that protect the various buildings these agencies are housed in, and spread that out over 5 years, you start to see that 450 million rounds really isn't that large of an order. Especially considering it is used for training purposes like firing range and live fire exercises, on-the-job use (though that is very limited), and to shore up their supplies. In fact, there are 65,000 – 70,000 law enforcement personnel at DHS who would be covered under this … ammunition contract. If DHS were to purchase all 450 million rounds over 5 years, then that would equate to only about 1,384 rounds of ammo per year per law enforcement [officer] … assuming the lower estimate of only 65,000 law enforcement personnel at DHS. Considering those agents go through training exercises several times per year, that is not a lot of ammunition. Perhaps most strangely, some have cited the purchase of hollow-point ammunition as evidence of the federal government's evil motives. Hollow-points are the defensive ammunition of choice for federal, state and local law enforcement officers across the country, just as they are for private citizens. These attacks are eerily similar to statements made by gun prohibitionists, who spent the much of the '70s, '80s and '90s complaining about "dum dum" bullets. (In fact, the Violence Policy Center's website still exhibits a publication lamenting that federal ammunition law "has no effect on today's generation of high-tech hollow-point ammunition.") The attacks also ignore the fact that federal agents, unlike average taxpayers on more limited budgets, normally train and qualify with their duty ammunition. As most gun owners will agree, skepticism of government is healthy. But today, there are more than enough actual threats to the Second Amendment to keep gun owners busy. With two key Supreme Court decisions hanging by a one-vote margin, the Justice Department deeply involved in a cover-up of a disastrous Mexican gun smuggling operation, and President Obama touting a ban on popular semi-automatic firearms, there is no need to invent additional threats to our rights. National Rifle Association of America. Institute for Legislative Action. This may be reproduced. /thread |
We can debate the reasoning and relevance ad nauseum. The real reason this is an issue, is that it is damned near impossible to find ammunition, and in particular hollow point ammo, for just about any reasonably common caliber. This would also appear to be a national concern, and not just a regional one.
I would have a difficult enough time believing this was nothing to worry about, if it was only impacting the major ammo manufacturers... However, it's not. It's impacting even the smaller and less known specialty ammunition manufacturers. The ammunition manufacturers are simply unable to keep the components in stock to manufacture ammunition. Until this is not the case, speculating on how reasonable these purchases are, and in particular when the fed gov't is able to obtain ammunition when the civilian populace is not... Under an administration that has made absolutely no bones about its desire to disarm the populace... This will continue to be an issue. Personally, I'm interested in keeping other people from building Utopia, because the more you believe you can create heaven on earth the more likely you are to set up guillotines in the public square to hasten the process. -- James Lileks
Last edited by Radeck; 05-05-2013 at 12:45 PM.. |
.. Christmas is a time when kids tell Santa what they want and adults pay for it. Deficits are when adults tell the government what they want and their kids pay for it.
Joe Biden says Buy a Shotgun! Wackiness ensues! [youtu.be] Are you on Obama's Little List? [youtube.com] Keynes vs Hayek economics rap battle [youtube.com] The biggest tax no one talks about [washingtontimes.com] "George Ought to Help" [youtube.com] How the GOP stole the 2012 nomination from Ron Paul [examiner.com] Save the internet, Save the world. |
While I will not deny that panic buying is definitely a serious part of the equation here, gov't involvement in purchasing is not anything to sneeze at, either. |
Maybe the Obama administration has decided to buy a ton of ammunition and sell them to tin-foil hat gun enthusiasts for a huge profit and then use the profit to secretly fund those programs that the Congress has defunded. You know, programs such as emergency heating oil help for the poor, etc.
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Kanye West's 25 Most Miserable Paparazzi Photos
It's no secret that Kanye West is not a big fan of the paparazzi. Even though he essentially invited them into his life by getting involved with Kim Kardashian last year, he has endured a number of run-ins with the paps over the years. Most recently, he yelled at a paparazzo who attempted to ask him a few questions at Los Angeles International Airport late last week. "Don't talk to me!" he screamed. "Don't talk to me at all, and don't talk to anyone I know!"
But that's not the only thing Kanye West has done to show his displeasure with the paparazzi. In addition to yelling at them, he's also given them absolutely nothing to work with in recent months. He always looks like someone just called and told him his Yorkshire died. Check out 25 of Kanye West's most miserable paparazzi photos. Prepare to be depressed.
Photo Credit: Nation


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Sensors 2009, 9(05), 3357-3375; doi:10.3390/s90503357
: A new closed-loop drive scheme which decouples the phase and the gain of the closed-loop driving system was designed in a Silicon Micro-Gyroscope (SMG). We deduce the system model of closed-loop driving and use stochastic averaging to obtain an approximate "slow" system that clarifies the effect of thermal noise. The effects of mechanical-thermal noise on the driving performance of the SMG, including the noise spectral density of the driving amplitude and frequency, are derived. By calculating and comparing the noise amplitude due to thermal noise both in the opened-loop driving and in the closed-loop driving, we find that the closed-loop driving does not reduce the RMS noise amplitude. We observe that the RMS noise frequency can be reduced by increasing the quality factor and the drive amplitude in the closed-loop driving system. The experiment and simulation validate the feasibility of closed-loop driving and confirm the validity of the averaged equation and its stablility criterion. The experiment and simulation results indicate the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise and as the driving mass decreases, the mechanical-thermal noise may get bigger than the electrical noise of the closed-loop driving circuitry.1. Introduction
The Silicon Micro-Gyroscope (SMG) is an important MEMS inertia sensor with a broad application in the national economy and defense fields [1-7]. These SMGs usually measure the proof-mass displacement by capacitive methods, but under normal atmospheric pressure, the minute moving proof-masses are especially susceptible to mechanical noise resulting from molecular agitation. Although accuracy is usually limited by electrical noise and systematic errors, mechanical thermal noise provides a theoretical lower limit for random errors [8-11]. Thus, a proper accounting of thermal noise is essential for the development of higher accuracy tactical and inertial grade gyroscopes.
The effects of mechanical-thermal noise on the sense-mode have been presented in the literature [8-11], but discussions of the effects of mechanical-thermal noise on drive-mode can hardly be found in the current literature. In this paper the effects of mechanical thermal noise on the driving performance of the SMG are mainly derived. Only the influence of the mechanical thermal noise is considered, while the electrical noise, sampling and quantization error, and distortion due to filtering are not considered. Meanwhile, we assume all the other processes run in an ideal manner. In this paper, a stochastic averaging approach is used to take account of the effects of closed-loop drive. The effect of mechanical thermal noise on drive-mode is discussed, then stochastic averaging is used to develop a model for the "slow" dynamics which represent the driving amplitude and frequency of the SMG. Both the steady-state and transient response of the model are obtained by stochastic averaging. The spectral density of the random error due to thermal noise on drive-mode is also derived.
2. Working Principle
As shown schematically in Figure 1(A), the micro-gyroscope consists of two silicon frames (outer-frame and inner-frame); the outer-frame is anchored on a glass substrate by six outer support beams and is connected with the inner-frame through four inner support beams. The outer-frame and the fixed interdigitated drive electrode on the glass substrate form the drive capacitors. The alternating drive force of the out-frame along the x-axis is generated through applying alternating current (AC) voltage with direct current (DC) bias voltage to the fixed drive electrode. Since the stiffness of the inner support beam along the x-axis (Kxi≫ Kx) is very large, the outer-frame and the inner-frame are driven together to vibrate along the x-axis by the alternating drive force, which causes the alternating capacitance between the outer-frame and fixed drive-sense electrode. We can capture the drive displacement by detecting the alternating capacitance. When the rotation rate along the z-axis is input, according to the Coriolis effect, the Coriolis force along the y-axis will be loaded on both the outer-frame and the inner-frame. Because the stiffness of the outer support beam along the y-axis (Kyo≫Ky) is very large, only the inner-frame is driven to vibrate along the y-axis by the Coriolis force, which induces the alternating capacitance between the inner-frame and fixed sense electrode. We can obtain the rotation rate along the z-axis by detecting the alternating capacitance.
The simplified motion equations of SMG are described by:
where x and y are separately the drive axis displacements and sense axis displacements in meters, Ω the rotation rate along the z-axis in radians/second, mx (mx=m1+m2) and my (my=m2) the drive proof mass and the sense proof mass in kilograms, Rx and Ry the damping in Newtons/meter/second, Kx and Ky the stiffness in Newtons/meter, and −2m xΩẋ the denote of the Coriolis force. Fe (Fe=Fdsinωdt) is the electrostatic force used to maintain the drive-mode vibration at a specified amplitude in terms of displacement, and at a resonant frequency of the drive-mode. Mechanical thermal noise on the drive axis is represented by the random force n(t), in units of force.Ignoring the influence of the random force n(t), the drive axis displacements and sense axis displacements in the steady state are described by:
where ; ; ; ; ωnx =(Kx/mx)(1/2); ωny =(Ky/my)(1/2); Qx=mxωnx/Rx, Qy=myωny/Ry.When ωd=ωnx=ωny, the maximum drive axis displacements and sense axis displacements are described by:
3. Mechanical Thermal Noise
Consider the damped harmonic oscillator:
The presence of damping in the system suggests that any oscillation would continue to decrease in amplitude forever. Inclusion of the fluctuating force n(t) prevents the system temperature from dropping below that of the system's surroundings. The damper provides a path for energy to leave the mass-spring system. This is the essence of the Fluctuation-Dissipation Theorem. According to Equipartition, if any collection of energy storage mode is in thermal equilibrium, then each mode will have an average energy equal to (1/2)kBT where kB is Boltzmann's constant(1.38×10-23J/K) and T is the absolute temperature in degrees Kelvin. A mode of energy storage is one in which the energy is proportional to the square of some coordinate; e.g., kinetic and spring potential.
When this system is in thermal equilibrium, the probability distribution of x and ẋ is given by equation (8):[12]
For the oscillator, the energy is the sum of the kinetic and spring potential energy:
From here, the equipartition theorem can be derived, namely that the mean energy in any energy storage mode is equal to(1/2)kBT. Thus:
where <·>denotes an ensemble average. The form of the distribution p(x, ẋ) indicates that x and ẋ are independent, Gaussian, and have zero mean. Since this holds for all values of mx and Kx, the thermal noise n(t) must be a white Gaussian noise with two sided spectral density [10]:The spectral density of drive displacements due to thermal noise is:
So the noise power spectrum is:
The RMS noise displacements due to thermal noise is:
According to Equation (5) and Equation (14) the signal-to-noise ratio of drive-mode is:
The above equation indicates that we can improve the signal-to-noise ratio by increasing the quality Qx and driving force amplitude Fd, or by reducing the stiffness and temperature.
4. Closed-loop Driving and System Model
As is known in the art of Coriolis force sensors, in order to achieve an acceptable response from the sensor, the proof mass vibration of the drive-mode should have a frequency at, or close to, the resonant frequency of the proof mass. At the same time, in order to improve the entire performance of the SMG, a high stability of the driving frequency and the amplitude of the drive-mode are needed. To satisfy those demands, the closed-loop driving of the drive-mode must be achieved. To this end, the drive signal has a frequency equal to the resonant frequency of the proof mass. However, parasitic capacitances between the drive electrode and the drive-sense electrode can cause significant errors. That is, when the drive signal capacitively couples into the drive-sense electrode, the accuracy of amplitude control by the feedback circuit is degraded and the harmonic frequency of the closed-loop system departs from the resonant frequency of the proof mass, resulting in less than optimum sensor performance, so we must eliminate the capacitive coupling. Various techniques are generally utilized in an effort to reduce capacitive coupling. In this paper, such a technique is utilized as follows: the drive electrode is arranged on the left, the drive-sense electrode is arranged on the right and the anchor of the SMG is connected with the ground or the virtual ground, which is shown in Figure 1(A). By separating the drive-sense interface (drive-sense electrode) from the interference source (drive voltage), we can reduce these capacitive couplings. Besides, the SMG studied in this paper is executed in vacuum encapsulation, with a working pressure under 10-1 Torr and the quality factor of the drive-mode above 2,500, which can also reduce these capacitive coupling by decreasing the drive voltage. The modulation-demodulation method through applying high-frequency carrier to the proof mass can also reduce these capacitive couplings.
First, we need to extract the resonance signal of the drive-mode. The simplified interface circuitry is shown in Figure 1. Figure 2 show the details of the interface circuit and the equivalent circuit. Here in Figure 2, C (t) is the alternating drive-sense capacitance, C(t)=C0+ΔC, C0 is constant capacitance. The part of signal sense can be equivalent to a current supply I(t) and a internal resistance C0 [see Figure 2(B)], where:
In Equation (16), the differential of driving capacitance to displacement Kxc is a constant relating to the structure. The capacitance C0 is very minute and generally has hundreds of fF, thus the impedance of C0 is very large and we can ignore the influence of the impedance C0. The resistance R1 generally has a few MΩ, the capacitance C1 hundreds of nF, ω/ 2ᴫ a few kHz (ω≈ωnx), so R1≫1/ωC1, the output voltage P(t) is described by:
Figure 3 is the frame of the closed-loop driving. In this figure s is a complex variable. Vs, Vref and Vsup are the direct current biases. L and J are the zero and the pole of the integrator separately. G is the gain of the integrator. In order to improve the precision and the stability of the closed-loop driving, the Q-factor of the drive-mode should be increased (the SMG is executed in vacuum encapsulation), while the well closed-loop control should be achieved. The closed-loop control must meet such two conditions: 1. The phase of the whole loop θ=2nπ (n is an integer); 2. The gain of the whole loop A>1.
A new closed-loop drive scheme which decouples the phase and the gain of the closed-loop driving system is adopted in the SMG, so that the phase and the gain can be optimized, respectively. The gain of the whole closed-loop system is controlled by the branch circuit above, and the phase is controlled by the branch circuit below. These two branch circuits respectively fulfill the two conditions of closed-loop control, adjusting and optimizing the closed-loop parameter separately. The "voltage comparator" is the key component of the closed-loop driving. The output of the "voltage comparator", with an invariable output amplitude, only reserves the phase information of the input signal, so the phase conditions of the closed-loop are isolated from the gain conditions. Except the drive mode of SMG and "voltage comparator", with the suppose that the phase of the other parts is fixed, when the phase of the "voltage comparator" is changed, the vibrating frequency of the closed-loop system will depart from the resonant frequency of the proof mass, so the phase condition controls the frequency of the driving displacement. It is obvious that the gain branch controls the amplitude of the driving displacement. According to Equations (34) and (35) (See Section 5), ignoring the influence of the random processes n1(t) and n2(t), we can know that average amplitude ā and average phase φ̄ are decoupled, so the phase branch and the gain branch can be optimized respectively and the new closed-loop drive scheme is succeeded.
To make sure that the harmonic frequency of the closed-loop system equals, or gets close to the resonant frequency of the proof mass, that is to say, the phase of the whole loop θ = 2nπ(n is an integer). When ωd=ωnx, the phase-shift of the drive displacement x(t) comparing to the drive force Fe is -π/2(See Equation (5)), the phase-shift of the output voltage of pre-amplifier P(t) comparing to drive displacement x(t) is -π/2 and the phase-shift of the output voltage of the "voltage comparator" Vcp(t) comparing to output voltage of preamplifier P(t) is −π. The other parts, which in fact all have tiny phase errors, have no phase-shifts, so the closed-loop control meets the phase conditions. In this way, it is hoped that the above closed-loop phase errors should be as tiny as possible. Various techniques are generally utilized in an effort to reduce closed-loop phase error, or drift, in servo circuits, such as amplifier circuits utilizing an operational amplifier. One such technique includes the addition of one or more zeros (i.e., a lead filter) in cascade with the open-loop gain of the operational amplifier in order to flatten the open-loop gain over a portion of the frequency band, generally resulting in only moderate closed-loop error reduction and also compromising stability. Another technique for reducing gain and phase errors is to increase the gain-bandwidth product associated with the operational amplifier. However, use of this technique is limited by the gain-bandwidth product of commercially available operational amplifiers as well as by the acceptable increased power dissipation associated with higher performance operational amplifiers. However, a Phase-Corrected Amplifier Circuit can be used to remove the closed-loop phase error [13]. An amplifier circuit having a bandpass circuit in cascade with the forward loop gain is provided, with the bandpass circuit having a transfer function approximating one plus a bandpass characteristic, the passband of which corresponds to the information band. This arrangement increases the open-loop gain of the amplifier circuit around the information frequency without affecting the open-loop gain at DC and crossover so as to reduce phase and gain errors around the information frequency.
In Figure 1, the drive capacitance and the electrical potential energy stored in the capacitance is described as:
where ε0 is the permittivity, h the thickness of the comb fingers, x0 the overlap length of the fingers, and d the width of the gap between fingers. According to Figure 3, the electrostatic drive force is described by: where is the differential of driving capacitance to displacement, the z(t) is a DC and Vcp(t) is a AC with the frequency near the resonant frequency ωnx. The first term of Equation (20) is a constant and does not contribute to the oscillating driving force. Since the amplitude of the AC driving voltage is chosen to be much smaller than the bias voltage, the third term of Equation (20) is much smaller than the second term and can be neglected. Therefore, under proper bias, the driving force is approximately proportional to the AC driving voltage.According to Figure 3, the drive-mode of the SMG is modeled as a second-order spring-mass-damper system with a dynamic behavior described by:
where Fn(u) is electrostatic drive force , and suppose z(t)≥0.Simplifying the integrator (See Figure 3) into the basic integral function, so:
i.e.: where |ẋ| is modulus of the driving velocity and:So the output of the "voltage comparator" is:
In summary, the entire closed-loop driving system, shown in Figure 3, are described by Equations (24)∼(25):
where Req is equivalent damper. Equations (24) and (25) show the closed-loop system model. With the ignorance of the influence of the random process n(t), Equation (24) shows a free spring-mass-damper oscillating system and Equation (25) shows the control principle of the integrator. The closed-loop system reduces the system damper Req through adjusting the output of the integrator z(t). When the equivalent damper Req is bigger than the zero(e.g.Req>0), the gain control loop reduces the output of the integrator z(t) and then the equivalent damper Req will decrease near the zero (Req≈0, is inverse-phase with Kxc). When the equivalent damper Req is smaller than the zero (e.g.Req<0), the gain control loop enhances the output of the integrator z(t) and thus, the equivalent damper will increase near the zero (Req≈0). So the closed-loop system shows approximately an undamped-free vibration with the invariable amplitude and frequency(e.g. the resonant frequency ωnx). However, the random process n(t) will influence the stability of the driving amplitude and frequency.5. Stochastic Averaging of the Gyroscope Dynamics
After the vacuum encapsulation, the quality factor of the drive-mode Qx becomes very big. The drive-mode of the SMG can be equivalent to a band-pass filter. Only the displacement with the resonant frequency ωnx can be magnified and the other harmonics are attenuated greatly. So the transient displacement can be simplified into a pure sin component. In order to analyze the transient behavior of the system, the driving displacement of the SMG is defined as [14]:
where a(t) is the amplitude, and φ(t) is the phase of the driving displacement signal respectively.
Differentiating Equation (26) with respect to time gives the velocity:
One of the equations used to determine a and φ is obtained by assuming that the sum of the last two terms can be set equal to zero:
Thus, the velocity equation becomes:
The acceleration is obtained by differentiating Equation (28) with respect to time:
Substituting Equations (26), (28) and (29) into Equation (24) yields:
Substituting Equation (28) into Equation (25), and suppose a≠0, according to Equation (27) and Equation (30), separate ȧ, φ̇ yields:
It should be noted that Equations (31)∼(33) are the exact differential equations describing the evolution of the amplitude and phase of the driving displacement, as well as that of the output states of the integrator. However, these equations are difficult to analyze because they are substantially non-autonomous. It is evident that instantaneous phase ωnxt evolves much faster than the other variables, such as a, φ, z and functions sin(ωnxt+φ) and cos(ωnxt+φ) are almost periodic. Within a period of these sinusoidal functions, variables other than ωnxt change very little. Hence, it is possible to apply the averaging method to the non-autonomous system described by Equations (31)∼(33) and approximate it by an autonomous system [14-15].
As pointed out above, instantaneous phase ωnxt is regarded as an independent variable and the differential equations Equations (31)∼(33) are averaged, with respect to ωnxt, over the interval [-π, π]. The averaged autonomous equations are:
where the bars denote averaged variables. The random processes n1(t) and n2(t) are independent white noise with the same intensity as n (t) [10]. Equations (34)∼(36) describe approximately how the displacement amplitude and phase evolve with time. According to Equations (34) and (35), it is evident that average amplitude ā and average phase φ̄ are decoupled – when one of them is changed, the other does not change, so the phase branch and the gain branch can be optimized respectively.Ignoring the influence of the random processes n1(t) and n2(t), the equilibrium of the averaged system described by Equations (34)∼(36) is:
When the power is switched on, the system stabilizes finally in equilibrium. According to Equation (37), it is evident that the equilibrium of the average amplitude āo is independent from the quality factor Qx, so the change of quality factor resulting from the variety of temperature and pressure does not impact on the equilibrium of the average amplitude āo, which is very important in the practical application. The speciality of this system is obviously different from the literature [16].
Ignoring the influence of the random processes n1(t) and n2(t), the Jacobian matrix of the nonlinear dynamic system of Equations (34)∼(36) at equilibrium is:
and its characteristic equation is: where γ is the variable of the characteristic equation. All the eigenvalues of the linearized averaged system are asymptotically stable, if and only if all coefficients is positive. It is evident Equation (40) satisfies this condition because is inverse-phase with Kxc. In order to make sure that the square root is in existence, the inequation hereinafter must be satisfied: i.e.: where the Vref is the referring DC voltage used as a reference to the amplitude of the pre-amplifier output voltage. The Vrefo is the criterion voltage. When Vref < Vrefo, the gain control branch works normally. When Vref >Vrefo, the gain control branch loses the control ability. Because the Equations (34)∼(36) are extremely complex, the averaged system is linearized in the equilibrium, i.e.: where ān = ā − āo, z̄n = z̄ − z̄o. ān can be expressed in Laplace transform domain as: where , Ān(s) is Laplace transform of ān, and N1(s) is Laplace transform of the n1, so the steady-state spectral density for the noise component of the ān is:So the noise power spectrum is:
The RMS noise amplitude due to thermal noise is:
Comparing Equation (14) with Equation (47), we know the RMS noise amplitude due to thermal noise in the opened-loop driving is equal to that in the closed-loop driving, so the closed-loop driving does not reduce the RMS noise amplitude due to thermal noise. By the way, the RMS noise amplitude is independent from the quality factor Qx.
According to ā = āo + ān ≈ āo, Equation (43) can be rewritten as:
where ω̄n is the noise frequency, so the power spectral density of the noise frequency ω̄n isSuppose the work bandwidth is fBHz, the noise power is:
The RMS noise frequency due to thermal noise is:
It is useful to reduce RMS noise frequency by increasing quality factor Qx and drive amplitude ā0.
6. Experiment and Simulation
6.1. Simulation
In order to validate the feasibility of closed-loop driving and confirm the validity of the averaged equation and its stable criterion, the closed-loop driving in Figure 3 is simulated according to parameters shown in Table 1. Figure 4 is the Matlab simulation frame of the closed-loop driving.
Figures 5 and 6 are the simulation curves for closed-loop driving when Vref = 0.5 < Vrefo and Vref = 0.7 > Vrefo [see Equation (41)]. It can be concluded from Figures 5(C) and 6(C) that the system resonant frequency approximately equals to the natural frequency of drive-mode after the system is stabilized, which indicates that the whole loop's phase θ = 2nл(n is an integer)and the phase branch circuit below is controlled accurately. When Vref < Vrefo, according to Figure 5 and Equation (37), the driving displacement goes along with the increase of Vref and the gain branch circuit above is controlled accurately. When Vref = Vrefo, the driving displacement reaches the maximum. When Vref increases persistently, that is to say, Vref > Vrefo, according to Figure 6, the output of the integrator z≈0 and the driving displacement does not go along with the increase of Vref and the gain branch circuit above does not work normally. The curve of the transient course of drive displacement along with the change of time goes smooth and the overshoot disappeares. Comparing Figure 5(A) to Figure 6(A), when Vref < Vrefo, we can see that the bigger the Vref is, the shorter the transient time is. When Vref > Vrefo, the above gain branch circuit does not work normally and the closed-loop system loses the adjustable ability, with the overshoot fading away.
Figures 7 and 8 are the simulated closed-loop response and averaged equation simulation curves when Vref = 0.3 < Vrefo and Vref = 0.7 > Vrefo. The simulation result indicates the envelope curve of the closed-loop response is basically the same as the curve of the averaged equation. The tiny differences come from the simplification of the integrator and truncation error in simulation. From Figure 8, when Vref = 0.7 > Vrefo, we can see that the envelope curve of the closed-loop response is also basically the same as the curve of averaged equation. Meanwhile, z ≈0, revealing that the above gain branch circuit does not work normally, which is in agreement with the practical situation. Thus, the averaged equation can be applied to the situations when Vref > Vrefo through the limit of the working scale of z(t).
In Figure 9, the simulation curves of closed-loop driving between Qx=2,500 and Qx=5,000 are compared. From Figure 9(A), we can see that although the quality factor increases, the amplitude of the driving displacement, which is in agreement with the conclusion derived from Equation (37), doesn't change. That is to say, the displacement amplitude has nothing to do with the quality factor. From Figure 9(B), we can see that the augment of quality factor results in the growth of output of the integrator z(t), which is accordant with the Equation (38). According to Equation (47) and Equation (51), when ωnx= 25,120 (rad/s), T=300 K, fB=100 Hz, Qx=2,500, āo = 5 μm, the influence of thermal noise on driving performance in different drive proof masses is shown in Figure 10. From Figure 10, we can see that the RMS noise displacement and the RMS noise frequency decrease with the increase of drive proof mass.
6.2. Experiment
The whole experiment circuit is constructed on the idea of Figure 3 and shown in Figure 11. The experiment results show that the SMG achieves closed-loop driving and the drive frequency works around the natural frequency of SMG all the time. The vibrating waveshape of the closed loop driving signal is shown in Figure 11(C). It is practical to find a better working point for SMG by adjusting z(t) in Figure 3. The experiment results of amplitude control with temperature are shown in Figure 12. According to the Equation (5), when ωd=ωnx, the amplitude of driving displacement is proportional with the quality factor Qx, so the change of quality factor, due to the variety of temperature and pressure, impacts directly on the amplitude of driving displacement in the open-loop driving. But the new closed loop driving is immunized to the change of the quality factor [see Equation (37) and Equation (47)]. With a temperature increase from -40°C to +40°C, the quality factor of the drive-mode Qx decreases about 2.6 times [see Figure 12(A)], while the drive amplitude signal increases by only 0.083% in the closed loop driving [see Figure 12(B)].
The experiment results of closed-loop driving are shown in Figure 13. Figure 13(A) and Figure 13(B) are the frequency drift and amplitude drift of driving signal for 1 h respectively. The experiment results show that the standard deviation of drive frequency is 0.0205 Hz, with relative drift 5.0 ppm, the standard deviation of the amplitude 0.0165 mV and relative drift 14.7 ppm, respectively. Figure 13(C) is the frequency spectrum of driving signal. The driving signal is about 100 dB bigger than the ground noise, which is accordance with the result of the Figure 13(B). As a result, both stabilities of driving frequency and amplitude are rather high and the closed loop control is very successful. According to Figure 10, when mx=2.89×10-7(kg), āo = 5um, ωnx= 25,120 (rad/s), we can find that the relative noise of drive frequency is approximately 0.0119 ppm and the relative noise of the amplitude is approximately 0.8 ppm, respectively. The noise comparison is shown in Table 2. So, in this situation, the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise. With the driving mass decreasing, the mechanical-thermal noise may get bigger than the electrical noise of closed-loop driving circuitry (see Figure 10).
7. Discussion and Conclusions
The mechanical thermal noise on drive-mode is discussed, and then stochastic averaging is used to develop a model for the "slow" dynamics that represent the driving amplitude and frequency of the SMG. Both the steady-state and transient response of the model are obtained by stochastic averaging. The spectral density of the random error due to thermal noise on drive-mode is also derived. By calculating and comparing the RMS noise amplitude due to thermal noise both in the opened-loop driving and in the closed-loop driving, we find that the closed-loop driving does not reduce the RMS noise amplitude. We observe that the RMS noise frequency can be reduced by increasing the quality factor and drive amplitude in the closed-loop driving system. The experiment and simulation validate the feasibility of closed-loop driving and confirm the validity of the averaged equation. The experiment and simulation results indicate the electrical noise of closed-loop driving circuitry is bigger than the mechanical-thermal noise and with the driving mass decreasing, the mechanical-thermal noise may get bigger than the electrical noise of closed-loop driving circuitry.
References and Notes
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Table 1. The value of simulation parameter. |
Parameter | value(unit) |
Qx | 2,500 |
Kxc | 2.92×10-8 (F/m) |
Vs | 10 (V) |
Vsup | 5 (V) |
Vrefo | 0.596 (V) |
|∂C/∂x| | 1.46×10-6 (F/m) |
ωnx | 25120 (rad/s) |
mx | 2.89×10-7 (kg) |
Table 2. The noise comparison. |
Simulation thermal noise | Measure noise(Driving signal) | ||||
mx = 2.89×10-7(kg), āo = 5μm, ωnx = 25,120 (rad/s) | |||||
Absolute value | Relative value | Absolute value | Relative value | ||
Thermal noise frequency | 0.0000476 Hz | 0.0119 ppm | Noise frequency | 0.0205 Hz | 5.0 ppm |
Thermal noise amplitude | 4×10-12 m | 0.8 ppm | Noise amplitude | 0.0165 mV | 14.7 ppm |
© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).


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